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1-lim-x-x-1-x-x-2-x-2-x-2-x-dx-2-2-xcos-2x-1-2x-cos-3x-dx-3-n-5-4n-3n-2n-




Question Number 186539 by test1234 last updated on 05/Feb/23
(1)∫(lim_(x→x+1) ((x^(x+2) x^(2+x^2 ) )/( (√x))))dx=?  (2)∫((2+xcos 2x)/(1−2x+cos 3x))dx=?  (3) Σ_(n=5) ^(4n) (3n+2n)=?
$$\left(\mathrm{1}\right)\int\left(\underset{{x}\rightarrow{x}+\mathrm{1}} {\mathrm{lim}}\frac{{x}^{{x}+\mathrm{2}} {x}^{\mathrm{2}+{x}^{\mathrm{2}} } }{\:\sqrt{{x}}}\right){dx}=? \\ $$$$\left(\mathrm{2}\right)\int\frac{\mathrm{2}+{x}\mathrm{cos}\:\mathrm{2}{x}}{\mathrm{1}−\mathrm{2}{x}+\mathrm{cos}\:\mathrm{3}{x}}{dx}=? \\ $$$$\left(\mathrm{3}\right)\:\underset{{n}=\mathrm{5}} {\overset{\mathrm{4}{n}} {\sum}}\left(\mathrm{3}{n}+\mathrm{2}{n}\right)=? \\ $$

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